A new three-dimensional point cloud data plane fitting implementation method

Abstract

The application discloses a new three-dimensional point cloud data plane fitting implementation method, characterized in that parameters of the method include input parameters and output parameters, the input parameters include that a three-dimensional point cloud set contains N space sample points, such as an i-th sample point p i =(x i y i z i ), T d : a threshold of variance screening, M: a point number of plane fitting selection, L: a plane fitting repetition number, and the output parameters include plane fitting coefficient fitting residual E l ; the application has the beneficial effect that machine vision technology is widely applied to various measurement detections in industrial automation, three-dimensional measurement is the most important in machine vision measurement, and plane fitting technology is widely used in three-dimensional measurement. The application helps to provide a method with excellent fitting effect and fitting speed.

Description

Technical Field

[0001] This invention relates to the field of algorithm application technology, specifically a new method for plane fitting of three-dimensional point cloud data. Background Technology

[0002] Currently, commonly used plane fitting algorithms include those based on the least squares principle and those based on the Random Sample Consensus (RANSAC) principle. These methods suffer from several drawbacks: significant interference from non-Gaussian noise and metallic reflective surfaces in point cloud data; poor least squares fitting performance; and excessively high computational complexity and low system efficiency of the RANSAC method. Therefore, a method that balances computational efficiency and performance is urgently needed.

[0003] Based on this, the present invention designs a new method for plane fitting of three-dimensional point cloud data to solve the above problems. Summary of the Invention

[0004] The purpose of this invention is to provide a new method for plane fitting of three-dimensional point cloud data to solve the problems mentioned in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution: a novel method for plane fitting of three-dimensional point cloud data, characterized in that the parameter description of the method includes input parameters and output parameters, wherein the input parameters include the three-dimensional point cloud set containing N spatial sample points, for example, the i-th sample point p i =(x i y i z i ), T d The output parameters include the variance screening threshold, M: the number of points selected for the fitting plane, and L: the number of repetitions for plane fitting. Fitting residual E I ;

[0006] The method includes the following steps:

[0007] Step 1: Randomly select the center of the circle to obtain the point cloud set of each cluster:

[0008] Randomly select K sample points from the point cloud space, and use sample point p i For example, take its x,y plane coordinates p′ i =(x i y i ), i∈[1 K] as the center of the region, the x-axis and y-axis directions must be symmetrical, and the range of values ​​for the set of points in the region is x∈[x i -dx i +d],y∈[y i -dy i+d], where the principle for choosing d is that the final number of point sets P satisfies:

[0009] With K regional centers, a total of K clusters of point clouds can be obtained;

[0010] Step 2: Generate the point cloud set ψ of the fitting plane:

[0011] Calculate the z-value of the point cloud samples contained in the i-th cluster. i，k The mean m i =E(z) i，k ) and variance d i =D(z) i，k ), i∈[1K], and the centroid of the cluster.

[0012] The threshold T for design variance d The variance d of a total of K clusters i In i∈[1 K], remove d i >T d The center of mass q i This yields a new set of centroids ψ.

[0013] For all sample points q in ψ j =(x j y j z j ), j∈[1 J], all satisfy d j ≤T d ;

[0014] Step 3: Fitting the plane:

[0015] M points are randomly selected from the point cloud set ψ, and plane fitting is performed according to the SVD decomposition method to obtain the plane fitting coefficients. And obtain the fitting residual E I ;

[0016] Repeat this step L times, selecting the plane fitting residual E. I Minimum plane coefficient As the final output plane value.

[0017] As a further technical solution of the present invention, the calculation background for generating the point cloud set ψ of the fitting plane is as follows: assuming (x0 y0 z0) is a point on the plane, according to the point normal equation of the plane, we have: a(x-x0)+b(y-y0)+c(z-z0)=0

[0018] After conversion, we can easily obtain: However, this is only an ideal situation, free from interference noise;

[0019] Taking the i-th cluster of point clouds as an example, rewriting the above equation yields the k-th point cloud on the same plane satisfying: z i，k =k1·x i，k +k2·y i，k +k c +e i，k ;

[0020] in, e i，k This represents the interference noise contained in the k-th sample point within the i-th point cloud cluster.

[0021] As a further technical solution of the present invention, the plane fitting method of the SVD decomposition method is as follows:

[0022] For J points q in the point cloud set ψ j =(x j y j z j Fit the plane equation;

[0023] make,

[0024] Construct the coefficient matrix

[0025] make The coefficients of the plane equation to be solved

[0026] The plane fitting algorithm is transformed into the following return-to-the-end problem:

[0027]

[0028] Abbreviated as:

[0029] ||A b||=0

[0030] st||b||2=1

[0031] Perform singular value decomposition on matrix A:

[0032]

[0033] Where U and V are orthogonal matrices, satisfying U T U = I.

[0034] ||A b||=||U∑V T b||=||U||||∑V T b||=||∑||||V T b||

[0035] ||V T b||=||b||=1

[0036] Since the diagonal elements of ∑ are singular values, assuming the last diagonal element is the smallest singular value, then ∑ is true if and only if:

[0037]

[0038] The plane error of matrix fitting is minimized;

[0039] Solve for the plane fitting coefficient vector b

[0040]

[0041]

[0042] Residual calculation:

[0043]

[0044] Compared with the prior art, the beneficial effects of the present invention are:

[0045] Machine vision technology is widely used in various measurement and inspection applications in industrial automation. Three-dimensional measurement is a crucial aspect of machine vision measurement.

[0046] Plane fitting is a widely used technique in 3D measurement. This patent helps to provide a method with both excellent fitting results and speed. Detailed Implementation

[0047] The technical solutions in the embodiments of the present invention will be clearly and completely described below. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0048] This invention provides a novel method for plane fitting of 3D point cloud data. The method includes input and output parameters. The input parameters include a 3D point cloud set containing N spatial sample points, such as the i-th sample point p. i =(x i y i z i ), T d The output parameters include the variance screening threshold, M: the number of points selected for the fitted plane, and L: the number of repetitions of the plane fitting. Fitting residual E I ;

[0049] The method includes the following steps:

[0050] Step 1: Randomly select the center of the circle to obtain the point cloud set of each cluster:

[0051] Randomly select K sample points from the point cloud space, and use sample point p i For example, take its x,y plane coordinates p′ i =(x i y i ), i∈[1 K] as the center of the region, the x-axis and y-axis directions must be symmetrical, and the range of values ​​for the set of points in the region is x∈[x i -dx i +d],y∈[y i -dy i +d], where the principle for choosing d is that the final number of point sets P satisfies:

[0052] With K regional centers, a total of K clusters of point clouds can be obtained;

[0053] Step 2: Generate the point cloud set ψ of the fitting plane:

[0054] Calculate the z-value of the point cloud samples contained in the i-th cluster. i，k The mean m i =E(z) i，k ) and variance d i =D(z) i，k ), i∈[1 K], and the centroid of the cluster.

[0055] The threshold T for design variance d The variance d of a total of K clusters i In i∈[1 K], remove d i >T d The center of mass q i This yields a new set of centroids ψ.

[0056] For all sample points q in ψ j =(x j y j z j ), j∈[1 J], all satisfy d j ≤T d ;

[0057] Step 3: Fitting the plane:

[0058] M points are randomly selected from the point cloud set ψ, and plane fitting is performed according to the SVD decomposition method to obtain the plane fitting coefficients. And obtain the fitting residual E I ;

[0059] Repeat this step L times, selecting the plane fitting residual E. I Minimum plane coefficient As the final output plane value.

[0060] Furthermore, the background for calculating the point cloud set ψ that generates the fitting plane is as follows: assuming (x0 y0 z0) is a point on the plane, according to the point normal equation of the plane, we have: a(x-x0)+b(y-y0)+c(z-z0)=0

[0061] After conversion, we can easily obtain: However, this is only an ideal situation, free from interference noise;

[0062] Taking the i-th cluster of point clouds as an example, rewriting the above equation yields the k-th point cloud on the same plane satisfying:

[0063] z i，k =k1·x i，k +k2·y i，k +k c +e i，k ;

[0064] in, e i，k This represents the interference noise contained in the k-th sample point within the i-th point cloud cluster.

[0065] Furthermore, the plane fitting method of the SVD decomposition method is as follows:

[0066] For J points q in the point cloud set ψ j =(x j y j z j Fit the plane equation;

[0067] make,

[0068] Construct the coefficient matrix

[0069] make The coefficients of the plane equation to be solved

[0070] The plane fitting algorithm is transformed into the following return-to-the-end problem:

[0071]

[0072] Abbreviated as:

[0073] ||A b||=0

[0074] st||b||2=1

[0075] Perform singular value decomposition on matrix A:

[0076]

[0077] Where U and V are orthogonal matrices, satisfying U T U = I.

[0078] ||A b||=||U∑V T b||=||U||||∑V T b||=||∑||||V T b||

[0079] ||V T b||=||b||=1

[0080] Since the diagonal elements of ∑ are singular values, assuming the last diagonal element is the smallest singular value, then ∑ is true if and only if:

[0081]

[0082] The plane error of matrix fitting is minimized;

[0083] Solve for the plane fitting coefficient vector b

[0084]

[0085]

[0086] Residual calculation:

[0087]

[0088] In the description of this specification, references to terms such as "an embodiment," "example," "specific example," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0089] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to the specific implementations described. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention. The invention is limited only by the claims and their full scope and equivalents.

Claims

1. A novel method for plane fitting of 3D point cloud data, characterized in that, The method's parameter description includes input parameters and output parameters. The input parameters include a 3D point cloud set containing N spatial sample points, and the i-th sample point. , The output parameters include the variance screening threshold, M: the number of points selected for the fitted plane, and L: the number of repetitions of the plane fitting. Fitting residuals ; The method includes the following steps: Step 1: Randomly select the center of the circle to obtain the point cloud set of each cluster: K sample points are randomly selected from the point cloud space. Take its coordinates in the x, y plane. As the center of the region, it must be symmetrical in both the x-axis and y-axis directions, and the range of values ​​for the set of points in the region is... , The selection principle is based on the final number of point sets. satisfy: ; With K regional centers, a total of K clusters of point clouds can be obtained; Step 2: Generate a set of point clouds for the fitting plane. : Calculate the point cloud samples contained in the i-th cluster. Get the mean With variance and the centroid of the cluster. ; Design variance threshold The variance of a total of K clusters In the middle, remove center of mass A new set of centroids is obtained. , for All sample points All satisfy ; Step 3: Fitting the plane: In point cloud collection M points are randomly selected from the data, and plane fitting is performed using the SVD decomposition method to obtain the plane fitting coefficients. And obtain the fitting residuals. ; Repeat this step L times, selecting the plane fitting residual. Minimum plane coefficient As the final output plane value.

2. The novel method for plane fitting of three-dimensional point cloud data according to claim 1, characterized in that, The point cloud set that generates the fitting plane The background for the calculation is as follows: Let be a point on a plane. According to the equation of the point-normal form of a plane, we have: After conversion, we can easily obtain: However, this is only an ideal situation and does not contain interference noise. Rewriting the above equation with the i-th cluster of point clouds, we obtain the k-th point cloud on the same plane, which satisfies: ; in, , , , This represents the interference noise contained in the k-th sample point within the i-th point cloud cluster.

3. The novel method for plane fitting of three-dimensional point cloud data according to claim 1, characterized in that, The plane fitting method of the SVD decomposition method is as follows: For point cloud collections In Points Fit the plane equation; make, , Construct the coefficient matrix make The coefficients of the plane equation to be solved The plane fitting algorithm is transformed into the following return-to-the-end problem: Abbreviated as: For matrix Perform singular value decomposition: in, , It is an orthogonal matrix that satisfies because If the diagonal elements are singular values ​​and the last diagonal element is the smallest singular value, then there exists a diagonal element with the following characteristics: The plane error of matrix fitting is minimized; Solving for the plane fitting coefficient vector Residual calculation: .

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